A sarashi is a long, winding strip of cloth, usually thick cotton, wrapped tightly around the midriff up to the chest. Historically, samurai wore them under their kimonos, to resist injury.
In anime series, a delinquent character, particularly in the classic older series, will be seen wearing one under their coat or unbuttoned shirt. The wrapping was a visible cue as to their general level of bad-assery.
A tomboyish girl may wear one to bind and/or flatten her breasts, especially if she is trying to pass as male. Alternatively, especially with kendo girls and other fighters, the wrapping may be a modified bra, wrapping only the chest area in a very nontraditional way.

(Copied from Danbooru)